On Feb 24, 1:09�pm, Lie <[EMAIL PROTECTED]> wrote: > On Feb 25, 1:21 am, Mark Dickinson <[EMAIL PROTECTED]> wrote: > > > On Feb 24, 1:09 pm, Lie <[EMAIL PROTECTED]> wrote: > > > > And this limit is much lower than n!. I think it's sum(primes(n)), but > > > I've got no proof for this one yet. > > > It's the least common multiple of the integers 1 through n, or > > equivalently the product over all primes p <= n of the highest power > > of p not exceeding n. �So for n = 100, it's: > > > 64 * 81 * 25 * 49 * 11 * 13 * 17 * ... rest of primes up to 100. > > > For general n, this number is of roughly the same order of magnitude > > as e**n. > > Ah, yes, I meant product(primes(n)), please forgive my honest mistake > which is partially caused by me not supposed to still be awake at this > time of the day. And thanks for Mark for noticing the mistake, and > here is the code I used: > > import fraction > import random > > frac = fraction.frac > ops = (frac.__add__, frac.__sub__) > > a = frac(random.randrange(1, 10), random.randrange(1, 10)) > b = frac(random.randrange(1, 10), random.randrange(1, 10)) > > while True: > � � o = ops[random.randrange(0, 2)] > � � a = o(a, b) > � � b = frac(random.randrange(1, 10), random.randrange(1, 10)) > � � print a > > I decided to keep the num/den limit low (10) because higher values > might obscure the fact that it do have limits. And through further > observations, I think it is sufficient if the limit is imposed in the > denominator only (numerator can have any values it wanted to, > denominator growth is determined only by the limit of denominator > growth). > > I think I'll also post the code for the fraction class I used, if you > have other fraction class that can automatically simplify, you could > use that instead as this class suffers from a naive GCD > implementation:
Out of curiosity, of what use is denominator limits? The problems where I've had to use rationals have never afforded me such luxury, so I don't see what your point is. -- http://mail.python.org/mailman/listinfo/python-list
